Date: 10/20/2003 at 11:18:10
From: Doctor Justin
Subject: Re: PSAT math problem
Hi Kevin,
This is a basic function problem that you will often run into when
taking the SAT or PSAT, so it is good to know how functions work.
Let's start with what a function actually is and does. A rough
definition of a function is a correspondence between two sets. This
means that when you input a number, exactly one other number will be
the output.
An example of a function is as follows:
P(x) = 2x
If you were to input 5 into the function, your output would be 10:
P(5) = 2*5 = 10
In my example, you can think of P as the name of the function, x
as the input, and 2x as the formula for the output. Functions have
many applications in mathematics, and the following item from our
archive provides a nice introduction to this notation:
What Is a Function?
http://mathforum.org/library/drmath/view/54545.html
In your problem, * is the name of the funtion, r is the input, and
(r + 2)/2 is the formula for the output. To find x you must first
input 4:
*4 = (4 + 2)/2 = 3
Thus, *4 = 3 and *4 = x so 3 = x.
We are trying to find *x, so substitute 3 into the function and you
should find the desired output.
Does this help?
- Doctor Justin, The Math Forum
http://mathforum.org/dr.math/